Higher-Matter and Landau-Ginzburg Theory of Higher-Group Symmetries

Abstract

Higher-matter is defined by higher-representation of a symmetry algebra, such as the $p$-form symmetries, higher-group symmetries or higher-categorical symmetries. In this paper, we focus on the cases of higher-group symmetries, which are formulated in terms of the strictification of weak higher-groups. We systematically investigate higher-matter charged under 2-group symmetries, defined by automorphism 2-representations. Furthermore, we construct a Lagrangian formulation of such higher-matter fields coupled to 2-group gauge fields in the path space of the spacetime manifold. We interpret such model as the Landau-Ginzburg theory for 2-group symmetries, and discuss the spontaneous symmetry breaking (SSB) of 2-group symmetries under this framework. Examples of discrete and continuous 2-groups are discussed. Interestingly, we find that a non-split 2-group symmetry can admit an SSB to a split 2-group symmetry, where the Postnikov class is trivialized. We also briefly discuss the strictification of weak 3-groups, weak 3-group gauge fields and 3-representations in special cases.

75 pages

References in corpus (40)

• Higher-Dimensional Algebra V: 2-Groups
• Universal Non-Invertible Symmetries
• Algebraic higher symmetry and categorical symmetry -- a holographic and entanglement view of symmetry
• Generalized Global Symmetries of $T[M]$ Theories. I
• The Global Form of Flavor Symmetries and 2-Group Symmetries in 5d SCFTs
• 2-Group Global Symmetries and Anomalies in Six-Dimensional Quantum Field Theories
• Higher Gauge Theory: 2-Connections on 2-Bundles
• Non-Invertible Symmetry Webs
• Higher-form symmetries of 6d and 5d theories
• Lecture Notes on Generalized Symmetries and Applications
• Higher-form symmetries and 3-group in axion electrodynamics
• 2-Group Symmetries in Class S
• Global 3-group symmetry and 't Hooft anomalies in axion electrodynamics
• 2-Group Symmetries and M-Theory
• Generalized Charges, Part I: Invertible Symmetries and Higher Representations
• 0-Form, 1-Form and 2-Group Symmetries via Cutting and Gluing of Orbifolds
• Mean string field theory: Landau-Ginzburg theory for 1-form symmetries
• Generalized symmetries and 2-groups via electromagnetic duality in AdS/CFT
• Codimension-2 defects and higher symmetries in (3+1)D topological phases
• Global 4-group symmetry and 't Hooft anomalies in topological axion electrodynamics
• Introduction to Generalized Global Symmetries in QFT and Particle Physics
• Higher-group symmetry in finite gauge theory and stabilizer codes
• Symmetries and Anomalies of (1+1)d Theories: 2-groups and Symmetry Fractionalization
• Higher representations for extended operators
• Disconnected 0-Form and 2-Group Symmetries
• 2-group global symmetries, hydrodynamics and holography
• Field theories with higher-group symmetry from composite currents
• Emergent generalized symmetries in ordered phases and applications to quantum disordering
• Disentangling supercohomology symmetry-protected topological phases in three spatial dimensions
• Higher-group symmetry of (3+1)D fermionic ${\mathbb{Z}}_2$ gauge theory: logical CCZ, CS, and T gates from higher symmetry
• Representation theory for categorical symmetries
• Bordism for the 2-group symmetries of the heterotic and CHL strings
• Higher-group structure in $2n$-dimensional axion-electrodynamics
• Topological aspects of brane fields: solitons and higher-form symmetries
• BCF anomaly and higher-group structure in the low energy effective theories of mesons
• Higher-group global symmetry and the bosonic M5 brane
• The 2-character theory of finite 2-groups
• A representation of the string 2-group
• The insidious bicategory of algebra bundles
• Central extensions of higher groups: Green-Schwarz mechanism and 2-connections